I develop conceptual models of the biogeochemistry and physical circulation of the Southern Ocean in order to study the air-sea fluxes of trace gases and biological productivity and their potential changes over glacial-interglacial timescales. Mesoscale eddy transfers play a dominant role in the dynamical and tracer balances in the Antarctic Circumpolar Current, and the transport of tracers is driven by the residual mean circulation which is the net effect of the Eulerian mean circulation and the eddy-induced circulation. Using an idealized, zonally averaged model of the ACC, I illustrate the sensitivity of the uptake of transient tracers including CFC11, bomb-[Delta]¹⁴C and anthropogenic CO₂ to surface wind stress and buoyancy fluxes over the Southern Ocean. The model qualitatively reproduces observed distribution of CFC11 and bomb-[Delta]¹⁴C , and a suite of sensitivity experiments illustrate the physical processes controlling the rates of the oceanic uptake of these tracers. The sensitivities of the uptake of CFC11 and bomb-[Delta]¹⁴C are largely different because of the differences in their air-sea equilibration timescales. The uptake of CFC11 is mainly determined by the rates of physical transport in the ocean, and that of bomb-[Delta]¹⁴C is mainly controlled by the air-sea gas transfer velocity. Anthropogenic CO₂ falls in between these two cases, and the rate of anthropogenic CO₂ uptake is affected by both processes. Biological productivity in the Southern Ocean is characterized with the circum- polar belt of elevated biological productivity, "Antarctic Circumpolar Productivity Belt".(cont.) Annually and zonally averaged export of biogenic silica is estimated by fitting the zonally averaged tracer transport model to the climatology of silicic acid using the method of least squares. The pattern of export production inferred from the inverse calculation is qualitatively consistent with recent observations. The pattern of inferred export production has a maximum on the southern flank of the ACC. The advective transport by the residual mean circulation is the key process in the vertical supply of silicic acid to the euphotic layer where photosynthesis occurs. In order to illustrate what sets the position of the productivity belt, I examined simulated biological production in a physical-biogeochemical model which includes an explicit ecosystem model coupled to the phosphate, silica and iron cycle. Simulated patterns of surface nutrients and biological productivity suggest that the circumpolar belt of elevated biological productivity should coincide with the regime transition between the iron-limited Antarctic zone and the macro-nutrients limited Subantarctic zone. At the transition, organisms have relatively good access to both micro and macro-nutrients. Kohfeld (in Bopp et al.; 2003) suggested that there is a distinct, dipole pattern in the paleo-proxy of biological export in the Southern Ocean at the LGM. I hypothesize that observed paleo-productivity proxies reflect the changes in the position of the Antarctic Circumpolar Productivity Belt over glacial-interglacial timescales. Increased dust deposition during ice ages is unlikely to explain the equatorward shift in the position of the productivity belt due to the expansion of the oligotrophic region and the poleward shift of the transition between the iron-limited regime and the macro-nutrient limited regime.(cont.) I develop a simple dynamical model to evaluate the sensitivity of the meridional overturning circulation to the surface wind stress and the stratification. The theory suggest that stronger surface wind stress could intensify the surface residual flow and perturb the position of the productivity belt in the same sign as indicated by the paleo-productivity proxies. Finally, I examined the relationship between the surface macro-nutrients in the polar Southern Ocean and the atmospheric pCO₂. Simple box models developed in 1980s suggests that depleting surface macro-nutrients in high latitudes can explain the glacial pCO₂ drawdown inferred from polar ice cores. A suite of sensitivity experiments are carried out with an ocean-atmosphere carbon cycle model with a wide range of the rate of nutrient uptake in the surface ocean. These experiments suggest that the ocean carbon cycle is unlikely to approach the theoretical limit where "pre- formed" nutrient is completely depleted due to the dynamics of deep water formation. The rapid vertical mixing timescales of convection preclude the ventilation of strongly nutrient depleted waters. Thus it is difficult to completely deplete the "preformed" nutrients in the Southern Ocean even in a climate with elevated dust deposition in the region, suggesting some other mechanisms for the cause of lowered glacial pCO₂.